I - . -.

k

,. i d

INVESTIGATION OF LASER DYNAMICS, MODULATION AND COWROL

BY MEANS OF INTRA-CAVITY TIME VARYING PERTURWTION

under t h e d i r e c t i o n of

S. E . Har r i s

Semi-Annual S ta tus Report No. 4

f o r

NASA Grant NGR-05-020-103

Nat iona l Aeronaut ics and Space Adminis t ra t ion

Washington, D . C .

f o r the pe r iod

1 August 1967 - 1 February 1968

M. L. Report No. 1617

February 1968

Microwave Laboratory W . W . Hansen Labora tor ies o f Phys ics

S tanford Un ive r s i ty Stanford, C a l i f o r n i a GPO PRICE $

- ff 653 J d y 6 5

- . i

I *

STAFF

E4 SA Gran t NGR -05 -0 20 - 10 3

f o r t h e per iod

1 A u g u s t 1967 - 1 F e b r u a r y 1968

PRINCIPAL INVESTIGATOR

S. E . Harris

PROFESS OR

A. E. Siegman

RE SEARCH ASS I STA l”T S

R . L. B y e r

J . F a l k

J. F. Young

J . E. M u r r a y

IDTRODUCTION

The work under t h i s g ran t i s gene ra l ly concerned w i t h t he genera t ion ,

cont ro l , and s t a b i l i z a t i o n of o p t i c a l frequency r a d i a t i o n . I n p a r t i c u l a r ,

we a r e now n e a r l y exc lus ive ly concerned w i t h a t t a i n i n g tunable o p t i c a l

sources by means of nonl inear o p t i c a l techniques. The p resen t p r o j e c t s

supported by t h i s g r a n t inc lude : (a ) an experimental and t h e o r e t i c a l

s tudy of a new type o f o p t i c a l r a d i a t i o n which we have termed as para-

metric f luorescence o r spontaneous emission;

a t ta inment of a paramet r ic o s c i l l a t o r employing a s t a b l e , phase-locked

gas l a s e r pumping source; and ( c ) a p r o j e c t whose goa l i s t h e demonstrat ion

of backward wave paramet r ic o s c i l l a t i o n wherein o p t i c a l r e sona to r s need

no t be employed, and wherein the output should be tunable over a l a r g e

r eg ion of t h e f a r i n f r a r e d spectrum.

(b) a p r o j e c t aimed a t t h e

During t h i s pe r iod the following p u b l i c a t i o n has been submitted

f o r pub li ca t ion

R. L. Byer and S. E. Harris, ' 'PO~~er and BmdTJidth of Spontaneous

Paramet r ic Emission, I ' t o be published i n Phys ica l Review.

The fo l lowing o r a l d i sc losu res have a l s o been presented :

S. E . Har r i s , R . L. Byer, and M. K . Oshman, "Power and Bandwidth of

Op t i ca l Paramet r ic Fluorescence," t h i r d n a t i o n a l Conference on

Nonlinear Opt ics , Erevan, Armenia, USSR, October. 1967.

- 1 -

. '

. . 4

*

PRESENT STATUS

l ( a ) . Opt ica l Parametr ic Fluorescence ( R . L . Byer and S. E. Harris)

The parametr ic f luorescence theory-experiment check has been com-

p l e t e d , and a paper has been accepted f o r pub l i ca t ion i n Phys ica l

Review. The r e s u l t s a r e presented below.

A t h e o r e t i c a l temperature tun ing curve was generated on the computer

a s ing the data of Hobden and Warner. F igure 1 shows t h a t t h e experiment

and theory agree w e l l . We found t h a t a l though the s lope of t h e curve

was t h e same f o r a l l c r y s t a l s measured, some curves were d i sp laced i n

temperature by a s much a s 30 C from the theory . This d i f f e r e n c e can

be a t t r i b u t e d t o d i f f e r e n c e s i n c r y s t a l i nd ices due t o c r y s t a l i m p u r i t i e s

and inhomogeneities

0

The predic ted l i n e a r r e l a t i o n s h i p between f luorescence power and

acceptance angle squared i s compared t o theory i n F ig . 2 . The d a t a

p o i n t s i n d i c a t e t h a t the experimental va lue of t he l i t h i u m n ioba te non-

l i n e a r i t y , d = 0.47 x 10 mks, i s s l i g h t l y l e s s than t h e publ i shed

va lue of 0.56 x 10

an important a p p l i c a t i o n of paramet r ic f luorescence .

advantages o f t h i s method r e l a t i v e t o second harmonic gene ra t ion a r e

f i r s t , t h a t t h e measurement i s independent of t h e a r e a o f t he pumping

beam, and second t h a t the r e s u l t i s dependent on ly on t h e average power

of the pumping l a s e r and independent of t h e commonly occur r ing temporal

f l u c tua t i m s .

-22 15

-22 mks. The measurement of c r y s t a l n o n l i n e a r i t y i s

Two important

- 2 -

. .

n

0 0 Y

w a 3 + Q a w e I w I-

- 3 -

FIG. Z--Total spontaneously emitted power vs Q2 showing theoretical and experimental results.

- 4 -

e

Theore t i ca l curves of f luorescence power a s a func t ion of frequency

f o r va r ious acceptance angles a re shown i n F ig . 3. The experimental

p o i n t s shown i n p a r t ( e ) v e r i f y t h e theo ry ve ry c l o s e l y . The bandwidth

ve r sus Q'

This curve shows t h a t t he bandwidth approaches a p red ic t ed minimum value

f o r small ang le s .

i s be l i eved t o be due t o c r y s t a l impur i t i e s which e f f e c t t h e ind ices .

curve of F ig . 4 presen t s t he da t a i n a more graphic form.

The q u a n t i t a t i v e disagreement of experiment and theory

A t p re sen t paramet r ic f luorescence i s proving v e r y va luab le f o r

determining t h e tun ing curves and n o n l i n e a r i t y of c r y s t a l s t o be used

i n t h e paramet r ic o s c i l l a t o r experiments.

l ( b ) . Fluorescence and Superradiance i n LiNbO Pumped a t X = 0 . 6 9 4 ~ 3 P (J . Falk, J, E . Murray, S . E. Harris)

The p o s s i b i l i t y of phase matching a 3-frequency down conversion

pa rame t r i c i n t e r a c t i o n i n LiNbO wi th a pump a t 0 . 6 9 4 ~ has been 3 po in ted out by Hobden and Warner.' During t h i s p a s t pe r iod we have

exper imenta l ly v e r i f i e d t h i s d i r e c t phase matching and obtained the

p o r t i o n of t h e phase matching curve between O.$ and 1.0~.

a t tempted t o exper imenta l ly demonstrate paramet r ic ga ins on t h e o rde r

of 30 dB w i t h t h i s p rocess . Unfortunately, m a t e r i a l problems have

made t h e r e s u l t s inconclus ive .

Also we have

The primary importance of t h i s process i s t h a t i t p o t e n t i a l l y

p rov ides v e r y high ga in which i s tunable from about 0.91 t o 4.01.

i s possi'ule f o r d i r e c t phase mtched p -o res s heca.use it. ~ O P S no t

This

J. Warner and M . V . Hobden, Phys. L e t t e r s 22, 243 (August 15, 1966). 1 -

- 5 -

3-

n - 'E ( d )

- - I

0

4- 4-

3 - ( e 1 3-

2 - 2 -

I -

e = 0.100

Y

( f 1

e =0.070

a" 1 1

-10 0 IO 20 30

. I . I

e

w

FIG. 3--Spectral d i s t r i b u t i o n of spontaneous power a t d i f f e r e n t acceptance angles . P a r t ( c ) shows experimental p o i n t s normalized t o peak of t he t h e o r e t i c a l curve.

- 6 -

. . . . 3 .

V

\ \ \

I I- n 3 n a m 7

\ \ 0 m 0

N 0 - 0

- 7 -

0 r e q u i r e frequency doubling of t he pump and thus makes p o s s i b l e much

higher pump d e n s i t i e s . These high ga ins would, f o r example, make i t

p o s s i b l e t o achieve o s c i l l a t i o n threshold w i t h ve ry wide band b u t l o s sy

cav i ty mirrors , g iv ing a source which would be tunable over a l a r g e

p o r t i o n of t h e near i n f r a r e d spectrum.

t h e need f o r r e sona t ing both t h e s i g n a l and i d l e r , thus avoid ing t h e

frequency hopping c h a r a c t e r i s t i c of c a v i t i e s which r e sona te bo th .

A l s o , high g a i n s would e l i m i n a t e

293

A l s o of importance i s t h e p o s s i b i l i t y of us ing t h i s process i n a tunable

i n f r a r e d ampl i f i e r .

The f i r s t experimental o b j e c t i v e was t o determine t h e tun ing curve

f o r t h e 3-frequency down conversion p rocess . The phase matching

condi t ions a r e the usua l ones f o r such a process :

w = w + u P S i

k = ks + ki P ,

where t h e subsc r ip t s p , i , and s r e f e r t o the pump, i d l e r , and

s i g n a l modes, r e s p e c t i v e l y . We w i l l d e f i n e t h e s i g n a l as t h a t mode

which tunes from degenerate a t 1.311 t o s h o r t e r wavelengths, because

t h i s i s the mode we d e t e c t e d exper imenta l ly . Tuning i s achieved b y

means of the temperature dependence of t he r e f r a c t i v e i n d i c e s of t h e

LiNbO c r y s t a l . 3 Using the da ta of Hobden and Warner, we obta ined t h e t h e o r e t i c a l

t un ing curve showr, i n F ig . 5 from a computer program. This curve guided

L J. A . Giordmaine and R . C . M i l l e r , Phys. Rev. L e t t e r s - 14, 973

(June 14 , 1965) . 'J. A. Giordmaine and R . C . Mi l l e r , A p p l . Phys . L e t t e r s - 9, 293

(1966) - 3 -

. . I . ..

8

e

[o L

0 0

0 9

0 \o c-

0 3 c-

0 cu t-

0 0 t-

.rl c -9

~ .rl 0 rl

- 9 -

u s t o t h e genera l temperature range f o r phase matching. Then, by

observ ing f luo rescen t emission produced by pumping w i t h about 10 kW/ cm 2

we obtained t h e tun ing curve shown i n F ig . 6 .

matching temperatures t o be about 40 K higher than those p red ic t ed by

We found t h e a c t u a l phase

0

theory . The wavelength of t h e emission was determined w i t h a Ze i s s

Monochrometer followed by a DuMont pho tomul t ip l i e r w i t h an S-1 su r face .

The monochrometer s l i t s were s e t t o g ive a r e s o l u t i o n of about 0 . 0 3 ~

which was a compromise between ease i n l o c a t i n g the s i g n a l and accuracy

of t he r e s u l t i n g phase matching curve. The experimental r e s u l t of

F ig . 6 a l s o shows the width of t he observed d e t e c t o r response, i nd ica t ed

by the s o l i d l i n e s a t t he da t a p o i n t s .

825 K, t h i s apparent wavelength spread i s due t o the monochrometer

r e s o l u t i o n ; b u t t h e p o i n t s above 325 K i n d i c a t e a v e r y apprec i ab le

f requency broadening i n t h e emission a s t h e i d l e r begins t o e n t e r t h e

For t h e 5 d a t a p o i n t s below

0

0

l o s s y region a t about 4.0~.

bandwidth fo r f l u o r e s c e n t emission a s g iven by Byer and H a r r i s .

This i s p red ic t ed by the t h e o r e t i c a l

4

The next experimental o b j e c t i v e was t o demonstrate t h e l a r g e ga ins

p red ic t ed by theory . The procedure used was t o monitor the s i g n a l power,

which r e s u l t e d from s i n g l e pass ga in of spontaneous s i g n a l power, as

the pump power d e n s i t y was inc reased . Thus, we expected t o s e e an

exponent ia l i nc rease i n s i g n a l power w i t h a l i n e a r i nc rease i n pump

power dens i ty .

I+ An extension of t h e f l u o r e s c e n t theory of Byer and H a r r i s r e s u l t e d

i n t h e fol lowing express ion f o r s i g n a l power d e n s i t y a s a func t ion of

4 R. L. Byer and S . E . Ha r r i s , Microwave Laboratory Report No. 1595, Stanford Univers i ty (November 1967); t o b e publ i shed i n Phys. Rev.

- 10 -

E u

0 Ln 0 Ln 0 m m a3 rl 0 d d

0 ;f x)

0 cr\ x)

0 (u x)

0 rl x)

0 0 x)

0 r n c-

0 ?

0 c- c-

0 a t-

- 11 -

beam radius :

where

Q = p o l a r acceptance angle i n the c r y s t a l

L = c r y s t a l l eng th

n = r e f r a c t i v e index of s i g n a l S

d = e l e c t r o - o p t i c coupling cons t an t .

Since we measured t o t a l power, i t was necessary t o i n t e g r a t e t h e

s i g n a l power d e n s i t y over t he assumed Gaussian c ros s s e c t i o n of t h e

pump :

The near f i e l d f o r our s e tup was a f a c t o r of 50 t imes longer than our

c r y s t a l so we neglec ted t h e v a r i a t i o n of pump d e n s i t y a long t h e beam

a x i s . Making a change of v a r i a b l e i n t h e above i n t e g r a l , we o b t a i n

- 12 -

L

I where B i s the c o l l e c t i o n of constants preceding t h e i n t e g r a l i n the

wi th I(0) given by the t o t a l pump power divided by i t s Gaussian a r e a .

F igure 7 shows the experimental r e s u l t s f o r one of our Limo3

c r y s t a l s . For t h i s p a r t i c u l a r c r y s t a l , t he e f f e c t i v e e l e c t r o - o p t i c

cons tan t was measured t o be

-22 d = 0.81 x 10 ( m k ~ ) ,

by SHG from X = 1.15~ . The c r y s t a l l eng th was 1.5 cm. Also shown

on t h e f i g u r e a r e the exponent ia l responses p red ic t ed by the above

equat ion and the l i n e a r response f o r t h i s c r y s t a l .

P

A s can be seen from the f igure , on ly a few of t h e experimental

p o i n t s a r e cons i s t en t w i t h t h e expected exponent ia l response. The upper

p o i n t s i n d i c a t e a ga in of about 27 dB. Most of t he o t h e r s a r e on o r

below the t h e o r e t i c a l l i n e a r response.

We a t t r i b u t e t h e po in t s , which seem t o i n d i c a t e a l i n e a r response,

t o c r y s t a l damage. We found t h a t we scorched t h e su r face of our c r y s t a l

w i t h

i n v a r i a b l y g ive p r o p o r t i o n a l l y smaller s i g n a l s . This i s cons i s t en t

w i t h t h e physics of t he i n t e r a c t i o n because the damaged a r e a s of t he

ci- j -s ta l would a c t t o d i f fuse the beam, des t .mying t .he plane wave

c h a r a c t e r of i t by d i s t r i b u t i n g i t s power throughout a l a r g e s o l i d

a n g l e . Since t h i s i n t e r a c t i o n w i l l accept only t h a t pump power wi th in

2 60 - 80 MW/cm , and t h a t subsequent sho t s a t t h i s same spot would

- 13 -

0

0

0

PUMP POWER (kW)

FIG. 7--Fluorescent power output as a f l m c t i o n of pump power. S o l i d l i n e i n - d i c a t e s t h e o r e t i c a l power output . polat . ion of t h e o r e t i c a l f l u o r e s c e n t power output .

Dashed l i n e i n d i c a t e s l i n e a r e x t r a -

- 14 -

k

a l i m i t e d p o l a r ang le t o pump a s ing le s i g n a l mode, t h i s d i f f u s e s c a t t e r i n g

would g r e a t l y

our d e t e c t i n g

m i l l i r a d i a n s , mo des.

reduce the e f f e c t i v e pump power pe r s i g n a l mode.

system had a reasonably narrow angular acceptance,

which would have prevented us from see ing o f f - ang le s i g n a l

Also,

QmaX = 2.24

I n conclusion, our da t a i s encouraging b u t n o t by any means

d e c i s i v e . We a r e hoping t o acqu i r e a good c r y s t a l of t he new nonl inear

m a t e r i a l Ba NaNb 0 . With t h i s c r y s t a l we can achieve the same ga in 2 5 15

l e v e l s w i t h only one-ninth of t h e pump power d e n s i t y r equ i r ed i n

Thus we hope t o avoid the damage problem we have encountered thus f a r .

It i s i n t e r e s t i n g t o no te t h a t w i t h s u f f i c i e n t l y good c r y s t a l s of

Limo3 .

BaZNaNb 0 it would be p o s s i b l e t o r each ga in l e v e l s high enough t o 3 15

ampl i fy spontaneous no i se power t o u s e f u l l e v e l s , r e s u l t i n g i n a tunable

supe r rad ian t source .

2. Parametr ic O s c i l l a t i o n a t Opt ica l Frequencies ( R . L. Byer, J . F. Young,

and S . E . Ha r r i s )

Components f o r t he i n t e r n a l argon pumped paramet r ic o s c i l l a t o r

desc r ibed i n t h e -previous r epor t have been completed and t e s t e d .

experiment was no t s u c c e s s f u l because of t he excess cav i ty l o s s i n t r o -

duced by t h e Limo w i t h i n the l a s e r cav i ty . Figure 8 shows t h e

rneasured abso rp t ion l o s s of LiNbO Power absorbed a t t h e l a s e r

pumping wavelength causes thermal s e l f - focus ing . The c r y s t a l l o c a l l y

h e a t s aiid becomes a h igh pa;;zr pGsi t ive l e n s 1.lrhtch d is rnpt . s t.he cav i ty

mode and makes i t extremely d i f f i c u l t t o o b t a i n high power i n the

fundamental Gaussian mode. The bes t observed l a s e r power a t 4800

The

3

3

- 15 -

ABSORPTION PERCENT PER CENTIMETER

LiNbO ABSORPTION

(UNPOLARIZED LIGHT ) 3

0 0

WAVELENGTH (8)

FIG. 8--Absorption l o s s i n Limo as a f i n c t i o n of wavelength. 3

- 16 -

. . .- 9 .

c-

e

was 1.5 watts, w e l l below the expected 4-5 w a t t s .

developed f o r t h i s i n t e r n a l o s c i l l a t o r was s d c c e s s f u l l y coated and

assembled.

The beam s p l i t t e r

I n t h e l a s t r e p o r t we descr ibed the f a i l u r e of t h e i n i t i a l krypton-

pumped e x t e r n a l paramet r ic o s c i l l a t o r because of poor c r y s t a l q u a l i t i e s .

Since then we have made considerable p rogres s i n the growing, po l ing ,

and t e s t i n g o f Limo c r y s t a l s , The c r y s t a l s a r e grown by the Mate r i a l

Science Department a t Stanford and poled by u s t o produce c r y s t a l s

having a s i n g l e f e r r o e i e c t r i c domain. A f t e r po l ing , fod r t e s t s a r e

used t o v e r i f y c r y s t a l q b a l i t y : usilai i n spec t ion between crossed p o l a r i z e r s

f o r s t r a i n ; measurement of e l e c t r o - o p t i c half-wave vo l t age ; measurement

of non l inea r c o e f f i c i e n t d by SHG; and measurement of t he temperature

tun ing curve us ing paramet r ic f luorescence, which a l s o provides an

independent measurement of d

3

15

15 All six c r y s t a l s which were poled a r e s t r a i n f r e e , b u t only t h r e e

have s a t i s f a c t o r y half-wave vo l t ages A poor half-wave vo l t age i s

be l i eved t o i n d i c a t e incomplete pol ing (multi-domain c r y s t a l ) and/or

l a r g e impuri ty concen t r a t ions? The SYG t e s t i s made by slowly va ry ing

c r y s t a l temperature wh i l e recording second harmofiic power output .

T h e o r e t i c a l l y t h i s power i s p ropor t iona l t o ( s i n M T / I k A T \ ) ' where k

i s a cons tan t and AT i s the temperature dev ia t ion from the exac t

phase-matching temperatdre . Figure 9 shows a SHG curve which ag rees

v e r y w e l l w i t h t h e theory . Second harmonic power i s generated only

over a ve ry narrow temperature range, and t h e va lue of d computed

from t h i s d a t a ag rees c l o s e l y w i t h the accepted l i t e r a t u r e va lue .

F i g u r e 10 shows a Cijrve t y p i c a l of t h e o t h e r two c r y s t a l s measured.

15

- 17 -

t .60°C

203 205 207

TEMPERATURE (DEGREES c )

3 FIG. 9--Second harmonic generat ion (1.15 p t o 0.575 p ) of LiNbO crystal No. 103, 1.7 cm long.

- 18 -

, .- . .

t

- 19 -

4' These longer c r y s t a l s genera te second harmonic power weakly over a

wide temperature range and a r e t h e r e f o r e not u se fu l . This type of

c r y s t a l prevented t h e krypton experiment from working. A t t h e p re sen t

t ime t h e cause o f t h i s smearing i s not known w i t h c e r t a i n t y , b u t i t i s

suspected to be due t o inhomogeneous inc lus ion of i m p u r i t i e s dur ing

growth.

and c r y s t a l #lo3 (F ig . 1) r e p r e s e n t s a 60% improvement i n l eng th over

ou r previous b e s t c r y s t a l . We a r e now t e s t i n g c r y s t a l s grown a long a

d i f f e r e n t a x i s which we hope w i l l y i e l d good c r y s t a l s 2 .5 t o 3 cm long .

Longer c r y s t a l s and t h e r e f o r e g r e a t e r paramet r ic ga in w i l l i nc rease t h e

o s c i l l a t i o n tun ing range a s w e l l a s ease a l l t h e c r i t i c a l t o l e rances i n

Long c r y s t a l s a r e p a r t i c u l a r l y susceptab le t o t h i s d i f f i c u l t y

the system.

Considering the h igh q u a l i t y of c r y s t a l #lo3 and t h e d i f f i c u l t i e s

of t he krypton experiment, we decided t o a t tempt t o cons t ruc t an e x t e r n a l

paramet r ic o s c i l l a t o r us ing the argon ion l a s e r 4880 l i n e as a pump.

The argon l a s e r i s g e n e r a l l y more s t a b l e than krypton and i t i s e a s i e r

t o o b t a i n high pumping powers.

longer .

I n a d d i t i o n t h e argon plasma tubes l a s t

Degenerate phase matching w i t h a 4880 a pump i s no t p o s s i b l e w i t h

Limo3

c a v i t y mirrors could b e made h igh ly r e f l e c t i n g a t s i g n a l and i d l e r

wavelengths s imultaneously.

t imes t h e s igna l wavelength, mir ror and a n t i - r e f l e c t i o n coa t ings can

be made which a r e a q u a r t e r wavelength t h i c k f o r t h e i d l e r and th ree -

q u a r t e r wavelengths t h i c k a t t h e s i g n a l - b o t h h i g h l y r e f l e c t i n g .

. Therefore a unique ope ra t ing p o i n t was chosen a t which the

By p ick ing t h e i d l e r wavelength t o be t h r e e

- 20 -

V

The cav i ty was cons t ruc ted and t e s t e d . The t o t a l e f f e c t i v e

(geometr ic mean) s i n g l e pass loss a t s i g n a l (6450 8) and i d l e r ( 2 . 0 0 ~ )

was 3%. This was low enough t h a t wi th a v a i l a b l e pump power the o s c i l l a t o r

was above threshold . The experiment was t r i e d bu t was not success fu l

f o r two reasons: (1) The LiNbO c r y s t a l thermal ly focused which

decreased t h e power coupled i n t o the cav i ty modes; and (2) we were

unable t o phase-lock the argon l a s e r a t 4880 a s u f f i c i e n t l y w e l l because

3

of t h e ve ry high excess ga in of t h a t l i n e . A f t e r eva lua t ing these

d i f f i c u l t i e s , we b e l i e v e the argon l i n e a t 5145 a w i l l be a more s u i t a b l e

pump. Because of i t s lower gain, it can be phase-locked ve ry s t rong ly .

This ga in more than compensates f o r t h e small l o s s i n output power

r e l a t i v e t o 4880 8. The parametr ic cav i ty mir rors a r e p r e s e n t l y be ing

coated f o r t h i s experiment. The thermal s e l f - focus ing e f f e c t w i l l be

somewhat reduced because of the lower c r y s t a l abso rp t ion a t 5145 a ( F i g . 8 ) . I n a d d i t i o n t h e time average power i n t o the LiNbO w i l l be

reduced w i t h a l i g h t chopper of s u i t a b l e duty cyc le .

3

Simultaneously w i t h the experimentalwork, a t h e o r e t i c a l a n a l y s i s

of t h e paramet r ic o s c i l l a t o r w i t h a phase-locked pump i s being done.

Th i s w i l l answer problems of mode competit ion, e f f e c t i v e peak power

a v a i l a b l e , and paramet r ic c a v i t y length to l e rances . I n add i t ion , t h e

problem of optimum pump focuss ing and c a v i t y des ign i s be ing s tud ied .

3. Backward Wave O s c i l l a t i o n i n the Far I n f r a r e d (J. Falk, J. E. Murray,

and S. E . Harris)

The purpose of t h i s p r o j e c t i s t o demonstrate a technique f o r

o b t a i n i n g l a r g e amounts of tunable f a r i n f r a r e d power. The b a s i c idea

- 21 -

i s t o make use of a backward wave i n t e r a c t i o n of t h r e e e lec t romagnet ic *.

waves which a r e coupled toge the r by means of t h e e l e c t r o - o p t i c non-

l i n e a r i t y .

The experiment a t tempted, as proposed i n S t a t u s Report 2, makes

use of a Q-switched ruby l a s e r and a c r y s t a l of L iTaO . For s u f f i c i -

e n t l y high pump d e n s i t i e s o p t i c a l c a v i t i e s f o r s i g n a l and i d l e r a r e no t 3

r equ i r ed and feedback i s provided i n t e r n a l l y t o t h e c r y s t a l . The

ca l cu la t ed threshold pump d e n s i t y f o r t h e 2.5 cm c r y s t a l used i n our

experimental e f f o r t s was 12 Mw/cm a

2 Severa l unsuccessfu l a t tempts were

2 made a t achieving o s c i l l a t i o n . Pump d e n s i t i e s of 70-125 Mw/cm , w i t h

pumping beam divergence of 10-20 m i l l i r a d i a n s were used.

F a i l u r e t o a t t a i n o s c i l l a t i o n th re sho ld i s a t t r i b u t e d t o l a s e r

beam divergence, i . e . , it was no t poss ib l e t o focus the l a s e r beam

down t o a spot s i z e t h a t would t h e o r e t i c a l l y be above threshold and

t h a t would have a divergence t h a t d id no t v i o l a t e k-vec tor synchronism.

Subsequent t o our experimental e f f o r t s an a n a l y s i s was c a r r i e d

out t o determine the a l lowable pump angular spread which could d r i v e

t h e parametr ic process .

The r e s u l t s o f t h i s a n a l y s i s show t h a t pump energy i n a p o l a r

angle given by

n n X X

ni XsL

2 P S P i tm = - ?

- 22 -

* . - .

I ’

n t n i , n a r e pump, i d l e r , and s i g n a l r e f r a c t i v e ind ices , P

Xp ? A s 7 Xi a r e pump, s igna l , and i d l e r wavelengths,

L i s c r y s t a l length, and

Xs > X. > X w i l l d r ive the backward wave process . 1 P

For t h e LiTaO pumped wi th ruby t h i s a l lowable divergence i s about

0.3 m i l l i r a d i a n s .

a r ea A and r a d i a t i n g uniformly i n t o an angle @ , where

g r e a t e r than flm given by E q . (1). By geometric o p t i c s any at tempt

t o f u r t h e r focus the pump w i l l l ead t o an inc rease i n divergence. Since

3 ( L = 2 ern , Xs = 0.35 mm) . Consider a l a s e r having

i s d, P P

i t s divergence i s a l r e a d y g r e a t e r than fl m , no f u r t h e r focusing of

t he pump i s p o s s i b l e and only a f r a c t i o n , @?@: , of the t o t a l power

d e n s i t y i s u s e f u l i n d r i v i n g the backward wave process .

The d e n s i t y i s t h e r e f o r e given by

T2 P

TP AP omax = Y-

n n A X 1 P P S P i - - -

n X ~ L P i P P

Hence 70 Mw/cm2 r a d i a t i n g i n t o 10 m i l l i r a d i a n s i s equiva len t t o about

100 kw/cm r a d i a t i n g w i t h i n @ m . Considerable e f f o r t has gone i n t o

t r a n s v e r s e mode c o n t r o l a s a means of reducing l a s e r beam divergence.

The use of a curved d i e l e c t r i c end mirror and a c a r e f u l l y se l ec t ed

a p e r a t u r e s top has provided us wi th a l a s e r which ope ra t e s w i th most

2

- 2 3 -

of i t s energy i n the lowest order (Gaussian) t r ansve r se cav i ty mode. +,

Far f i e l d beam divergence has been reduced t o l e s s than 0 .4 m i l l i r a d i a n s .

Output spot s i z e i s about

1 Mw.

cm2 and output power i s g r e a t e r than

Wi th the l a s e r pump e s s e n t i a l l y i n the lowest order t r ansve r se

mode the highest a l lowable focus ing i s d i c t a t e d by t h e requirement t h a t

t he s igna l , i d l e r , and pump beams overlap i n the c r y s t a l . This l i m i t s

focusing t o Rayleigh range a t t he f a r i n f r a r e d wavelength

or approximately 10 cm . Hence the g r e a t e s t a v a i l a b l e pumping

( A L/2ns) S -2 2

d e n s i t y i s approximately 100 Mw/cm2 o r more than e i g h t t imes threshold

f o r a non-cavity backward wave o s c i l l a t o r .

A s a f i r s t s t e p toward c a v i t y f r e e o s c i l l a t i o n i n t h e f a r i n f r a r e d

we propose t o resonate the i d l e r , thus only r e q u i r i n g ga in t o overcome

cav i ty l o s s e s . Calcu la ted threshold f o r round t r i p cav i ty l o s s of

15% i s approximately 1 . 2 Mw/cm . of the proposed experiment.

2 See F ig . 11 f o r a schematic o u t l i n e

If s i n g l e c a v i t y backward wave o s c i l l a t i o n i s experimental ly

success fu l we w i l l measure paramet r ic gain by i n s e r t i o n of l o s s i n t o

t h e i d l e r cav i ty j u s t s u f f i c i e n t t o quench the o s c i l l a t i o n . If measured

parametr ic gain i s s u f f i c i e n t f o r c a v i t y f r e e backward wave o s c i l l a t i o n

the i d l e r cav i ty w i l l be removed and the c a v i t y f r e e experiment w i l l be

a t temp t ed . Previous b i r e f r ingence versus temperature measurements show t h a t

tuning should be p o s s i b l e from below the lowest Raman mode (1.33 microns)

t o a wavelength g r e a t e r than 1 mm. See F ig . 1 2 .

- 24 -

c .

I .

ffi w kl 0 PI

I

a a, v) 0 PI 0

$ I

r i

- 25 -

3 LiTaO A S

(MILLIMETERS )

0.4-

0.6-

0.8-

1.0-

1 . 2 -

1.6-

0.4- CALCULATED PHASE MATCHING

SIGNAL BACKWARD WAVE

0.8-

1.0-

1.6-

I I I I I I 1 300 320 340 360 380 400 420 440 460 480

K 0

CALCULATED PHASE MATCHING

SIGNAL BACKWARD WAVE

FIG. 12--Calculated phase matched s i g n a l wavelength, LiTaO pumped with ruby. of birefr ingence versus temperature.

This curve i s based on a 6328 R meas&ement

- 26 -

\ ,

, t.

./

Although previous problems of po l ing LiTaO have been solved, 3 some d i f f i c u l t y remains i n the a q u i s i t i o n of good o p t i c a l q u a l i t y

c r y s t a l s . A problem i s a n t i c i p a t e d i n acqu i r ing c r y s t a l s whose

b i r e f r i n g e n c e does not wander along the length . This e f f e c t has been

found t o be severe i n LiNbO and i s expected i n LiTaO . 3 3

- 27 -